# Special theory of relativity  (Page 8/9)

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$x\prime =\gamma \left(x-vt\right)$

Lorentz factor appears in most of the relativistic equations including the calculation of relativistic effects like time dilation, length contraction, mass etc. An understanding of the beahviour of this factor at different relative velocity is intuitive for assessing the extent of relativistic effect. Few values of Lorentz factor are tabulated here.

Lorentz factors
Speed (v) 0 0.1c 0.2c 0.3c 0.4c 0.5c 0.6c 0.7c 0.8c 0.9c 0.99c 0.999c
Lorentz factor (γ) 1.000 1.005 1.021 1.048 1.091 1.115 1.250 1.400 1.667 2.294 7.089 22.366

Lorentz factor begins at 1 and as v->c, y->infinity. It is either equal to 1 or greater than 1. In other words, it is never less than 1. A plot of Lorentz factor .vs. relative speed is shown here.

## Space-time interpretation

We identify an event with spatial (x,y,z) and temporal (t) coordinates. Important point is that an event does not belong to any reference. It is described by different coordinates in different reference system. In classical description, spatial and temporal parameters are essentially independent of each other. The time t of an event can not be dependent on spatial specification (x,y,z,). Now, this independence is not there in relativistic kinematics. In order to imbibe the nature of space time relation, we shall work with few Lorentz transformations here.

We interpret an event in two inertial references which are moving with respect to each other at a velocity say 0.3c in x-direction. We shall consider very small time interval like 0.000005 second so that distance involved is easy to visualize. For convenience, we consider the approximate value of speed of light 300000000 m/s. In time 0.000005 s, the separation of two reference frame at the speed 0.3c works out to be 0.3 X 300000000 X 0.000005 = 450 m.

Here, we calculate both Galilean and Lorentz distance and time of events in two references for events identified in first reference by x and t values. Unprimed values refer to stationary reference, whereas primed values refer to moving reference which is moving right in x-direction with a relative velocity 0.3c. The calculations have been done using Excel worksheet (Reader can also try and verify the results) where distance is in meters and time in seconds.

Lorentz factors
x t x’(Galilean) t’(Galilean) x’(Lorentz) t’(Lorentz)
0 0 0 0 0 0
2 0.000005 -448 0.000005 -469.6317 0.0000052393
100 0.000005 -350 0.000005 -366.8998 0.0000051366

Since the origins of two references coincide for both Galilean and Lorentz transformations at t= t’=0, the space and time values are all zero as shown in the first row of the table.

Let us now consider the second row of the table. Here, position of event is x=2 m at time, t = 0.000005 s. In this time, primed reference has moved 450 m. According to Galilean transform, the event takes place at -450+2 = -448 m (to the left of origin) in the moving reference. Since time is invariant in Galilean transformation, the time of event is same in moving reference for non-relativistic Galilean transformation. However, when we employ relativistic Lorentz transformation, the event occurs at -469.6317 m (to the left of origin) in the moving reference. Here, the measurement of distance in moving reference is different than that calculated with Galilean transformation. Also, time is not invariant. The event occurs at 0.0000052393 s in this reference instead of 0.000005 s in the unprimed stationary reference. Thus, we see that both space and time are not invariant in Lorentz transformation.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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